Question 57486
Are the following lines parallel, perpendicular, or neither?
   L1 with equation x – 4y = 12
   L2 with equation 4x + y = 4
Putting equations is slope intercept form {{{highlight(y=mx+b)}}}, m=slope, (0,b)=y-intercept, makes it easy to see their slopes.  Parallel lines have = slopes, perpendicular lines have slopes that are negative reciprocals (opposite signs and upside down), if they aren't either of those, it's neither.
L1) x-4y=12
-x+x-4y=-x+12
-4y=-x+12
-4y/-4=-x/-4+12/-4
y=(1/4)x-3  The slope of L1, m=1/4
L2) 4x+y=4
-4x+4x+y=-4x+4
y=-4x+4  The slope of L2 is m=-4/1
The slopes are negative reciprocals of each other, therefore the lines are perpendicular.